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/* sgtsvx.f -- translated by f2c (version 20061008).
You must link the resulting object file with libf2c:
on Microsoft Windows system, link with libf2c.lib;
on Linux or Unix systems, link with .../path/to/libf2c.a -lm
or, if you install libf2c.a in a standard place, with -lf2c -lm
-- in that order, at the end of the command line, as in
cc *.o -lf2c -lm
Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
http://www.netlib.org/f2c/libf2c.zip
*/
#include "f2c.h"
#include "blaswrap.h"
/* Table of constant values */
static integer c__1 = 1;
/* Subroutine */ int sgtsvx_(char *fact, char *trans, integer *n, integer *
nrhs, real *dl, real *d__, real *du, real *dlf, real *df, real *duf,
real *du2, integer *ipiv, real *b, integer *ldb, real *x, integer *
ldx, real *rcond, real *ferr, real *berr, real *work, integer *iwork,
integer *info)
{
/* System generated locals */
integer b_dim1, b_offset, x_dim1, x_offset, i__1;
/* Local variables */
char norm[1];
extern logical lsame_(char *, char *);
real anorm;
extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *,
integer *);
extern doublereal slamch_(char *);
logical nofact;
extern /* Subroutine */ int xerbla_(char *, integer *);
extern doublereal slangt_(char *, integer *, real *, real *, real *);
extern /* Subroutine */ int slacpy_(char *, integer *, integer *, real *,
integer *, real *, integer *), sgtcon_(char *, integer *,
real *, real *, real *, real *, integer *, real *, real *, real *,
integer *, integer *);
logical notran;
extern /* Subroutine */ int sgtrfs_(char *, integer *, integer *, real *,
real *, real *, real *, real *, real *, real *, integer *, real *,
integer *, real *, integer *, real *, real *, real *, integer *,
integer *), sgttrf_(integer *, real *, real *, real *,
real *, integer *, integer *), sgttrs_(char *, integer *, integer
*, real *, real *, real *, real *, integer *, real *, integer *,
integer *);
/* -- LAPACK routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* SGTSVX uses the LU factorization to compute the solution to a real */
/* system of linear equations A * X = B or A**T * X = B, */
/* where A is a tridiagonal matrix of order N and X and B are N-by-NRHS */
/* matrices. */
/* Error bounds on the solution and a condition estimate are also */
/* provided. */
/* Description */
/* =========== */
/* The following steps are performed: */
/* 1. If FACT = 'N', the LU decomposition is used to factor the matrix A */
/* as A = L * U, where L is a product of permutation and unit lower */
/* bidiagonal matrices and U is upper triangular with nonzeros in */
/* only the main diagonal and first two superdiagonals. */
/* 2. If some U(i,i)=0, so that U is exactly singular, then the routine */
/* returns with INFO = i. Otherwise, the factored form of A is used */
/* to estimate the condition number of the matrix A. If the */
/* reciprocal of the condition number is less than machine precision, */
/* INFO = N+1 is returned as a warning, but the routine still goes on */
/* to solve for X and compute error bounds as described below. */
/* 3. The system of equations is solved for X using the factored form */
/* of A. */
/* 4. Iterative refinement is applied to improve the computed solution */
/* matrix and calculate error bounds and backward error estimates */
/* for it. */
/* Arguments */
/* ========= */
/* FACT (input) CHARACTER*1 */
/* Specifies whether or not the factored form of A has been */
/* supplied on entry. */
/* = 'F': DLF, DF, DUF, DU2, and IPIV contain the factored */
/* form of A; DL, D, DU, DLF, DF, DUF, DU2 and IPIV */
/* will not be modified. */
/* = 'N': The matrix will be copied to DLF, DF, and DUF */
/* and factored. */
/* TRANS (input) CHARACTER*1 */
/* Specifies the form of the system of equations: */
/* = 'N': A * X = B (No transpose) */
/* = 'T': A**T * X = B (Transpose) */
/* = 'C': A**H * X = B (Conjugate transpose = Transpose) */
/* N (input) INTEGER */
/* The order of the matrix A. N >= 0. */
/* NRHS (input) INTEGER */
/* The number of right hand sides, i.e., the number of columns */
/* of the matrix B. NRHS >= 0. */
/* DL (input) REAL array, dimension (N-1) */
/* The (n-1) subdiagonal elements of A. */
/* D (input) REAL array, dimension (N) */
/* The n diagonal elements of A. */
/* DU (input) REAL array, dimension (N-1) */
/* The (n-1) superdiagonal elements of A. */
/* DLF (input or output) REAL array, dimension (N-1) */
/* If FACT = 'F', then DLF is an input argument and on entry */
/* contains the (n-1) multipliers that define the matrix L from */
/* the LU factorization of A as computed by SGTTRF. */
/* If FACT = 'N', then DLF is an output argument and on exit */
/* contains the (n-1) multipliers that define the matrix L from */
/* the LU factorization of A. */
/* DF (input or output) REAL array, dimension (N) */
/* If FACT = 'F', then DF is an input argument and on entry */
/* contains the n diagonal elements of the upper triangular */
/* matrix U from the LU factorization of A. */
/* If FACT = 'N', then DF is an output argument and on exit */
/* contains the n diagonal elements of the upper triangular */
/* matrix U from the LU factorization of A. */
/* DUF (input or output) REAL array, dimension (N-1) */
/* If FACT = 'F', then DUF is an input argument and on entry */
/* contains the (n-1) elements of the first superdiagonal of U. */
/* If FACT = 'N', then DUF is an output argument and on exit */
/* contains the (n-1) elements of the first superdiagonal of U. */
/* DU2 (input or output) REAL array, dimension (N-2) */
/* If FACT = 'F', then DU2 is an input argument and on entry */
/* contains the (n-2) elements of the second superdiagonal of */
/* U. */
/* If FACT = 'N', then DU2 is an output argument and on exit */
/* contains the (n-2) elements of the second superdiagonal of */
/* U. */
/* IPIV (input or output) INTEGER array, dimension (N) */
/* If FACT = 'F', then IPIV is an input argument and on entry */
/* contains the pivot indices from the LU factorization of A as */
/* computed by SGTTRF. */
/* If FACT = 'N', then IPIV is an output argument and on exit */
/* contains the pivot indices from the LU factorization of A; */
/* row i of the matrix was interchanged with row IPIV(i). */
/* IPIV(i) will always be either i or i+1; IPIV(i) = i indicates */
/* a row interchange was not required. */
/* B (input) REAL array, dimension (LDB,NRHS) */
/* The N-by-NRHS right hand side matrix B. */
/* LDB (input) INTEGER */
/* The leading dimension of the array B. LDB >= max(1,N). */
/* X (output) REAL array, dimension (LDX,NRHS) */
/* If INFO = 0 or INFO = N+1, the N-by-NRHS solution matrix X. */
/* LDX (input) INTEGER */
/* The leading dimension of the array X. LDX >= max(1,N). */
/* RCOND (output) REAL */
/* The estimate of the reciprocal condition number of the matrix */
/* A. If RCOND is less than the machine precision (in */
/* particular, if RCOND = 0), the matrix is singular to working */
/* precision. This condition is indicated by a return code of */
/* INFO > 0. */
/* FERR (output) REAL array, dimension (NRHS) */
/* The estimated forward error bound for each solution vector */
/* X(j) (the j-th column of the solution matrix X). */
/* If XTRUE is the true solution corresponding to X(j), FERR(j) */
/* is an estimated upper bound for the magnitude of the largest */
/* element in (X(j) - XTRUE) divided by the magnitude of the */
/* largest element in X(j). The estimate is as reliable as */
/* the estimate for RCOND, and is almost always a slight */
/* overestimate of the true error. */
/* BERR (output) REAL array, dimension (NRHS) */
/* The componentwise relative backward error of each solution */
/* vector X(j) (i.e., the smallest relative change in */
/* any element of A or B that makes X(j) an exact solution). */
/* WORK (workspace) REAL array, dimension (3*N) */
/* IWORK (workspace) INTEGER array, dimension (N) */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* > 0: if INFO = i, and i is */
/* <= N: U(i,i) is exactly zero. The factorization */
/* has not been completed unless i = N, but the */
/* factor U is exactly singular, so the solution */
/* and error bounds could not be computed. */
/* RCOND = 0 is returned. */
/* = N+1: U is nonsingular, but RCOND is less than machine */
/* precision, meaning that the matrix is singular */
/* to working precision. Nevertheless, the */
/* solution and error bounds are computed because */
/* there are a number of situations where the */
/* computed solution can be more accurate than the */
/* value of RCOND would suggest. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Parameter adjustments */
--dl;
--d__;
--du;
--dlf;
--df;
--duf;
--du2;
--ipiv;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
x_dim1 = *ldx;
x_offset = 1 + x_dim1;
x -= x_offset;
--ferr;
--berr;
--work;
--iwork;
/* Function Body */
*info = 0;
nofact = lsame_(fact, "N");
notran = lsame_(trans, "N");
if (! nofact && ! lsame_(fact, "F")) {
*info = -1;
} else if (! notran && ! lsame_(trans, "T") && !
lsame_(trans, "C")) {
*info = -2;
} else if (*n < 0) {
*info = -3;
} else if (*nrhs < 0) {
*info = -4;
} else if (*ldb < max(1,*n)) {
*info = -14;
} else if (*ldx < max(1,*n)) {
*info = -16;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SGTSVX", &i__1);
return 0;
}
if (nofact) {
/* Compute the LU factorization of A. */
scopy_(n, &d__[1], &c__1, &df[1], &c__1);
if (*n > 1) {
i__1 = *n - 1;
scopy_(&i__1, &dl[1], &c__1, &dlf[1], &c__1);
i__1 = *n - 1;
scopy_(&i__1, &du[1], &c__1, &duf[1], &c__1);
}
sgttrf_(n, &dlf[1], &df[1], &duf[1], &du2[1], &ipiv[1], info);
/* Return if INFO is non-zero. */
if (*info > 0) {
*rcond = 0.f;
return 0;
}
}
/* Compute the norm of the matrix A. */
if (notran) {
*(unsigned char *)norm = '1';
} else {
*(unsigned char *)norm = 'I';
}
anorm = slangt_(norm, n, &dl[1], &d__[1], &du[1]);
/* Compute the reciprocal of the condition number of A. */
sgtcon_(norm, n, &dlf[1], &df[1], &duf[1], &du2[1], &ipiv[1], &anorm,
rcond, &work[1], &iwork[1], info);
/* Compute the solution vectors X. */
slacpy_("Full", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx);
sgttrs_(trans, n, nrhs, &dlf[1], &df[1], &duf[1], &du2[1], &ipiv[1], &x[
x_offset], ldx, info);
/* Use iterative refinement to improve the computed solutions and */
/* compute error bounds and backward error estimates for them. */
sgtrfs_(trans, n, nrhs, &dl[1], &d__[1], &du[1], &dlf[1], &df[1], &duf[1],
&du2[1], &ipiv[1], &b[b_offset], ldb, &x[x_offset], ldx, &ferr[1]
, &berr[1], &work[1], &iwork[1], info);
/* Set INFO = N+1 if the matrix is singular to working precision. */
if (*rcond < slamch_("Epsilon")) {
*info = *n + 1;
}
return 0;
/* End of SGTSVX */
} /* sgtsvx_ */
|
